Question 1135043: Find a polynomial function that has the given zeros and whose graph passes through the point. Zeros : 3, -2, 4 Point (0,3)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The given Zeros are 3, -2, 4 then
:
(x-3) * (x+2) * (x-4) = 0
:
(x^2 -x -6) * (x-4) = 0
:
x^3 -5x^2 -2x +24 = 0
:
The general form of this polynomial passing through (0,3) is
:
a * (x^3 -5x^2 -2x +24) = y
:
substitute 0 for x and 3 for y
:
a * (0^3 -5*0^2 -2*0 +24) = 3
:
24a = 3
:
a = 3/24 = 1/8
:
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p(x) = (x^3 -5x^2 -2x +24)/8
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